A fluid velocity measurement system consists of a pitot tube, a differential pressure trans$-$

mitter, an $8-$bit analogue$-$to$-$digital converter and a microcontroller with display facilities.

Table Prob. $6$ gives the model equations and parameters for each element in the system. The

microcontroller calculates the measured value of velocity assuming a constant density.

$($a$)$ Estimate the mean and standard deviation of the error probability density function

assuming the true value of velocity $v_T$ is $14\mathrm{.}0m{s}^{-1}.$ Use the procedure of Table $3\mathrm{.}1,$

treating the rectangular distributions as normal with $=\frac{h}{\sqrt[\phantom{2}]{3}}.$

$($b$)$ Explain briefly what modifications could be made to the system to reduce the quanti$-$

ties calculated in $($a$).$